Varieties of K-lattices

TL;DR

This paper explores varieties of commutative residuated lattices constructed via twist-products, extending classical lattice concepts to a broader algebraic framework with recent interest.

Contribution

It introduces new varieties of residuated lattices derived from twist-product constructions, expanding understanding of their algebraic properties.

Findings

Characterization of varieties obtained from twist-products

Extension of classical lattice concepts to residuated lattices

New algebraic properties identified for these varieties

Abstract

In this paper we deal with varieties of commutative residuated lattices that arise from a specific kind of construction: the {\em twist-product} of a lattice. Twist-products were first considered by Kalman in 1958 to deal with order involutions on plain lattices, but the extension of this concept to residuated lattices has attracted some attention lately. Here we deal mainly with varieties of such lattices, that can be obtained by applying a specific twist-product construction to varieties of integral and commutative residuated lattices.